Mrs. Gomez is a mother to 2 boys. The number of children she has is three times the number of boys she has. Her children are planning to buy her a bouquet of flowers. What is the biggest bouquet they can buy in which the ratio of pink flowers to blue flowers matches the ratio of girls to boys if the florist has 9 blue carnations and 12 pink carnations left?

a bouquet of 12 flowers, 4 pink and 8 blue
a bouquet of 14 flowers, 8 pink and 6 blue
a bouquet of 15 flowers, 6 pink and 9 blue
a bouquet of 18 flowers, 12 pink and 6 blue

1 answer

Let's first find out how many children Mrs. Gomez has in total. We know that she has 2 boys. The problem states that the number of children she has is three times the number of boys. Therefore, we can set up the following equation:

Let \( B \) = number of boys = 2
Let \( C \) = number of children

From the problem, we have:
\[ C = 3B \]
Substituting the value for \( B \):
\[ C = 3 \times 2 = 6 \]

Therefore, Mrs. Gomez has a total of 6 children. Since she has 2 boys, she must have:
\[ G = C - B = 6 - 2 = 4 \]
So she has 4 girls.

Now we have:

  • Number of girls (G) = 4
  • Number of boys (B) = 2

Next, we calculate the ratio of girls to boys:
\[ \text{Ratio of girls to boys} = \frac{G}{B} = \frac{4}{2} = 2:1 \]

Now we can see which bouquet matches the 2:1 ratio of pink flowers to blue flowers.

Let's evaluate the provided bouquet options:

  1. Bouquet of 12 flowers: 4 pink and 8 blue

    • Ratio = \( \frac{4}{8} = \frac{1}{2} \) (Not 2:1)
  2. Bouquet of 14 flowers: 8 pink and 6 blue

    • Ratio = \( \frac{8}{6} = \frac{4}{3} \) (Not 2:1)
  3. Bouquet of 15 flowers: 6 pink and 9 blue

    • Ratio = \( \frac{6}{9} = \frac{2}{3} \) (Not 2:1)
  4. Bouquet of 18 flowers: 12 pink and 6 blue

    • Ratio = \( \frac{12}{6} = 2 \) (This equals 2:1)

The largest bouquet that matches the girl's to boy's ratio of 2:1 is:

The bouquet of 18 flowers, 12 pink and 6 blue.